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Majorons and Supernova Cooling

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Majorons and Supernova Cooling Novell).ber 29, 1989 CMU-HEP89-23 MPI-PAE/PTh 75/89 ' Majorons and Supernova Cooling 1 2 Kiwoon Choi ) and A. Santan1aria* ) 1 ) Department of Physics, Carnegie Mellon University Pittsburgh, PA 15213, USA 2 ) Max-Planck-Institut fiir Physik und Astrophysik Fahringer Ring 6, D-8000 Miinchen 40, Germany Abstract We consider the role of majoron emission in supernova cooling and its implications for the neutrino mass and lifetime in generic singlet majoron models. It is found that for v, with mass m, if the lifetime for the decay v, ...... majoron + v .... is shorter than 10-7(m/MeV) sec, then majorons are so strongly trapped by the inverse process that the resulting majoron luminosity is small enough to not destabilize the observed v.-pulse from SN1987 A. For v, with a longer lifetime, the majoron luminosity can be large enough to destroy or significantly shorten the duration of the neutrino pulse. We then find the range of paran1eters, e.g. the v,-mass m and the B- L breaking scale v, that is excluded by giving such a large majoron luminosity. Our results imply that, for v between 1 GeV and 1 TeV, a wide range of m allowed by terrestrial experiments can be excluded in view of the observed v.-pulse from SN1987 A. *Permanent address: Departament de Fisica TeOrica, Universitat de Valencia and IFIC, Universitat de Valencia-CSIC, Spain. 1. Introduction The supernova SN1987 All] in the Large Magelanic Cloud has provided a lot of information on the properties of neutrinos, e.g. masses, number of generationsl2l, mag­ 3 4 8 netic momentsl l, and exotic interactionsl - l. One clear observation associated with SN1987A is the thermal neutrino pulse (more precisely v.-pulse) which is considered to carry off most of the gravitational binding energy of the resulting neutron star. As a result, any exotic interaction of neutrinos must be tuned to not destabilize this neutrino pulse. 9 13 In majoron modelsl - l, where neutrinos have nonzero Majorana masses due to the spontaneous B - L violation, there exist exotic interactions of neutrinos with the Higgs fields, in particular with the massless majoron component ¢>, that trigger the spontaneous B - L violation. The implications of these additional interactions for the dynamics of supernova neutrinos have already been considered by many authors. The energy release by majoron emission may significantly shorten the duration of the neutrino pulse from supernovael6 ,7J. Too much neutrino-majoron scattering inside the supernova core would delay neutrino emissionl8l. Also the scattering between supernova neutrinos and cosmic background majorons will lead to an energy loss for the neutrinos and thus effectively stops them being detectedl4l. Among these implications, in this paper, we will concentrate on the role of majoron emission in the cooling of the hot nascent neutron star associated with SN1987A. In Ref. 6, the emission of majorons from supernovae through the process vv --> ¢>¢> has been considered with the assumption that only the coupling of the form h¢>vi"(sV is responsible for the majoron production process, viz all other majoron couplings were assumed to be weak enough. Then it was found that for a majoron-neutrino Yukawa 2 5 4 coupling h in the range 0(10- )::::; h ::::;0(10- ), the majoron luminosity dominates over the neutrino luminosity, which seems to be inconsistent with the observed neutrino pulse from SN1987 A. However as we will see in Appendix C, the assumption made in Ref. 6 is valid only for a special range of parameters as is the corresponding conclusion about h. The matter-induced decay v --. v</> was discussed in Ref. 7 as another process that produces majorons inside the supernova core, however only for neutrinos with m ~ GFYn (Yn=number density of nucleons inside the supernova). Furthermore none of the above mentioned papers provided a complete analysis of the possible trapping of majorons. Although the authors of Ref. 6 took into account the process <f>v -t </>v and the matter-induced majoron absorption <f>v -t v was con­ siderd in Ref. 7, there always exists a possibility that majorons are strongly trapped by other processes. Then in order to find the forbidden region of the parameter space where the majoron luminosity is large enough to destablize the neutrino pluse from SN1987 A, one should take into account all the processes that may trigger the trapping of majorons. Note that if majorons are strongly trapped by anyone of the processes under consideration, the resulting majoron luminosity will be small and will not affect the neutrino pulse regardless of the strength of the other processes. It is therefore tempting to analyze supernova cooling via majoron emission in a fully general co~text, particularly to analyze the effects of all the possible majoron interactions on the trap­ ping of majorons inside the supernova core. The purpose of this paper is to provide such an analysis. For majoron models in which the massless majoron belongs mainly to an elec­ 12 13 troweak non-singlet Higgs field[ • 1, e.g. the triplet model of Gelrnini and Roncadelli, majorons are strongly trapped by the weak neutral current interactions with back­ ground nucleons. Furthermore in such models, the global U(l)B.:.L symmetry is prob- 3 ably restored inside the supernova core since the astrophysical bound on the majoron­ electron coupling[14•15l (see eq.(2)) gives a severe constraint on the B- L breaking scale v, viz v ~ 0(10) KeV~ T (T=core temperature of the supernova). Thus, through­ out this paper, we consider only models in which the majoron belongs mainly to an electrowea.k singlet Higgs field[•-nJ. Note that the magnitude of v in generic singlet majoron models is not highly constrained and can be arbitrarily large compared to the core temperature of the supernova. Majoron emission from hot stars must be constrained in view of the long burning time scale. Among the various majoron couplings that induce majoron production, the role of the majoron electron coupling of the form (1) has been studied well (together with the axion coupling of the same form) and leads to the upper bound[14•15l (2) Although this bound strongly constrains the scale v in gauge non-singlet majoron mod­ els by v ~ 0(10) KeV, it says little about singlet majoron models since it is easily satisfied for the natural values of parameters in the theory. One unique property of the majoron is that it can have relatively strong interactions with the neutrino while keeping the couplings to ordinary matter, e.g. electrons or nucleons, weak enough to satisfy the astrophysical bound of eq.(2). Furthermore, the coupling of the majoron to neutrinos is simply determined by the neutrino mass m and thus any information about it can be translated .. and the B- L breaking scale v, into a constraint on either m or v. It would therefore be very interesting to have an astrophysical constraint on the majoron interactions with neutrinos. Then supernovae 4 provide a unique way to get astrophysical information about the majoron-neutrino coupling, because of the presence of the thermal neutrino spheref16l that contains a high density of neutrinos for a relatively long time scale of 5 ~ 10 sec. Majoron emission from SN1987Af17l can also be constrained by the observed neu­ trino pulse. It is generally believed that the remnant of SN1987 A was a neutron star whose gravitational binding energy has an upper limit of 6 x 1053 erg. The relatively long time scale (t = 5 ~ 10 sec) of the neutrino flux with total energy Efot = (1 ~ 4)x1053 erg then severely constrains majoron emission. H the majoron luminosity L¢ was greater than 1053 erg/sec, the neutrino pulse would be affected significantly, perhaps enough to be inconsistent with the observed neutrinos. In this paper, as a conservative bound, we will take 3 x 1053 erg/sec as the maximum allowed majoron luminosity, viz Lif> ::::; 3 x 1053 erg/ sec, (3) and try to find the parameter region excluded by eq.(3). This simple approaclt has turned out to be a good approximation to a more careful analysis including the effects of majoron emission on the detailed models for supernova dynamicsf18l. H majorons interact with background particles so weakly that the majoron mean free path 1¢ is greater than the radius r0 of the inner core, then majorons will freely stream out from the supernova. In this case, the majoron luminosity L¢ is proportional to the majoron creation rate times the volume of the hot core region (volume emission). The total creation rate for freely escaping majorons is a simple sum of the partial creation rates for eaclt of the relevant processes. Then in considering the parameter range that gives L¢ ;::: 3 x 1053 erg/sec, one can consider only a particular set of interesting processes without worrying about the role of the other processes. The corresponding range of parameters must be ruled out regardless of the ignored processes. For relatively strong majoron couplings that give I¢ < r 0 , majorons are trapped inside 5 the supernova core and form a thermal sphere of radius R¢ at which the majoron optical depth is of order unity. Then L.p can be approximated by blackbody emission from this majoron sphere (blackbody surface emission). A crucial point in the case of surface emission is that one must take into account all of the processes that are potentially relevant to majoron trapping in order to find the parameter region excluded by giving 53 L.p ;?: 3 X 10 erg/sec. The organization and summary of this paper are as follows. First of all, in Sec.
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